{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# https://people.duke.edu/~ccc14/sta-663/MCMC.html\n",
    "from __future__ import division\n",
    "import os\n",
    "import sys\n",
    "import glob\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as st\n",
    "\n",
    "%matplotlib inline\n",
    "%precision 4\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.0000e+000,   4.3606e-113,   8.2531e-095,   3.7324e-084,\n",
       "         1.2782e-076,   8.5319e-071,   4.7159e-066,   4.6702e-062,\n",
       "         1.3134e-058,   1.4119e-055,   7.1059e-053,   1.9352e-050,\n",
       "         3.1731e-048,   3.3975e-046,   2.5300e-044,   1.3774e-042,\n",
       "         5.7084e-041,   1.8611e-039,   4.9056e-038,   1.0696e-036,\n",
       "         1.9665e-035,   3.1000e-034,   4.2496e-033,   5.1286e-032,\n",
       "         5.5078e-031,   5.3133e-030,   4.6428e-029,   3.7017e-028,\n",
       "         2.7108e-027,   1.8340e-026,   1.1523e-025,   6.7567e-025,\n",
       "         3.7128e-024,   1.9194e-023,   9.3690e-023,   4.3318e-022,\n",
       "         1.9027e-021,   7.9615e-021,   3.1814e-020,   1.2168e-019,\n",
       "         4.4643e-019,   1.5742e-018,   5.3444e-018,   1.7500e-017,\n",
       "         5.5355e-017,   1.6939e-016,   5.0211e-016,   1.4437e-015,\n",
       "         4.0311e-015,   1.0943e-014,   2.8910e-014,   7.4404e-014,\n",
       "         1.8672e-013,   4.5729e-013,   1.0939e-012,   2.5578e-012,\n",
       "         5.8503e-012,   1.3098e-011,   2.8725e-011,   6.1741e-011,\n",
       "         1.3014e-010,   2.6916e-010,   5.4651e-010,   1.0899e-009,\n",
       "         2.1360e-009,   4.1154e-009,   7.7983e-009,   1.4540e-008,\n",
       "         2.6683e-008,   4.8216e-008,   8.5819e-008,   1.5051e-007,\n",
       "         2.6016e-007,   4.4336e-007,   7.4513e-007,   1.2353e-006,\n",
       "         2.0209e-006,   3.2627e-006,   5.2000e-006,   8.1833e-006,\n",
       "         1.2718e-005,   1.9525e-005,   2.9614e-005,   4.4385e-005,\n",
       "         6.5744e-005,   9.6261e-005,   1.3934e-004,   1.9943e-004,\n",
       "         2.8226e-004,   3.9510e-004,   5.4706e-004,   7.4930e-004,\n",
       "         1.0154e-003,   1.3614e-003,   1.8063e-003,   2.3716e-003,\n",
       "         3.0818e-003,   3.9636e-003,   5.0458e-003,   6.3585e-003,\n",
       "         7.9319e-003,   9.7955e-003,   1.1976e-002,   1.4496e-002,\n",
       "         1.7372e-002,   2.0613e-002,   2.4216e-002,   2.8167e-002,\n",
       "         3.2439e-002,   3.6990e-002,   4.1761e-002,   4.6680e-002,\n",
       "         5.1660e-002,   5.6602e-002,   6.1396e-002,   6.5928e-002,\n",
       "         7.0079e-002,   7.3737e-002,   7.6793e-002,   7.9155e-002,\n",
       "         8.0746e-002,   8.1509e-002,   8.1413e-002,   8.0454e-002,\n",
       "         7.8654e-002,   7.6060e-002,   7.2745e-002,   6.8802e-002,\n",
       "         6.4341e-002,   5.9484e-002,   5.4358e-002,   4.9091e-002,\n",
       "         4.3806e-002,   3.8616e-002,   3.3622e-002,   2.8906e-002,\n",
       "         2.4534e-002,   2.0551e-002,   1.6986e-002,   1.3849e-002,\n",
       "         1.1134e-002,   8.8240e-003,   6.8915e-003,   5.3020e-003,\n",
       "         4.0166e-003,   2.9951e-003,   2.1973e-003,   1.5852e-003,\n",
       "         1.1241e-003,   7.8307e-004,   5.3557e-004,   3.5943e-004,\n",
       "         2.3653e-004,   1.5252e-004,   9.6307e-005,   5.9497e-005,\n",
       "         3.5932e-005,   2.1194e-005,   1.2197e-005,   6.8418e-006,\n",
       "         3.7363e-006,   1.9840e-006,   1.0230e-006,   5.1150e-007,\n",
       "         2.4759e-007,   1.1583e-007,   5.2269e-008,   2.2707e-008,\n",
       "         9.4750e-009,   3.7881e-009,   1.4471e-009,   5.2666e-010,\n",
       "         1.8198e-010,   5.9481e-011,   1.8313e-011,   5.2865e-012,\n",
       "         1.4232e-012,   3.5519e-013,   8.1617e-014,   1.7132e-014,\n",
       "         3.2555e-015,   5.5415e-016,   8.3458e-017,   1.0960e-017,\n",
       "         1.2333e-018,   1.1643e-019,   8.9885e-021,   5.4956e-022,\n",
       "         2.5559e-023,   8.5857e-025,   1.9455e-026,   2.7111e-028,\n",
       "         2.0408e-030,   6.8628e-033,   7.6797e-036,   1.7461e-039,\n",
       "         3.1986e-044,   5.9186e-051,   1.4662e-062,   0.0000e+000])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import scipy.stats as stats\n",
    "from functools import partial\n",
    "\n",
    "np.random.seed(1234)\n",
    "n = 100\n",
    "h = 61\n",
    "p = h/n\n",
    "rv = st.binom(n, p)\n",
    "mu = rv.mean()\n",
    "\n",
    "a, b = 10, 10\n",
    "prior = st.beta(a, b)\n",
    "post = st.beta(h+a, n-h+b)\n",
    "ci = post.interval(0.95)\n",
    "\n",
    "thetas = np.linspace(0, 1, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAAIuCAYAAACb0U+yAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e39a690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 9))\n",
    "plt.style.use('ggplot')\n",
    "plt.plot(thetas, prior.pdf(thetas), label='Prior', c='blue')\n",
    "plt.plot(thetas, post.pdf(thetas), label='Posterior', c='red')\n",
    "plt.plot(thetas, n*st.binom(n, thetas).pmf(h), label='Likelihood', c='green')\n",
    "plt.axvline((h+a-1)/(n+a+b-2), c='red', linestyle='dashed', alpha=0.4, label='MAP')\n",
    "plt.axvline(mu/n, c='green', linestyle='dashed', alpha=0.4, label='MLE')\n",
    "plt.xlim([0, 1])\n",
    "plt.axhline(0.3, ci[0], ci[1], c='black', linewidth=2, label='95% CI');\n",
    "plt.xlabel(r'$\\theta$', fontsize=14)\n",
    "plt.ylabel('Density', fontsize=16)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAAIuCAYAAACb0U+yAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110c78b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0, 1, 200)\n",
    "prior = st.beta(a, b)\n",
    "\n",
    "post = prior.pdf(thetas) * st.binom(n, thetas).pmf(h)\n",
    "post /= (post.sum() / len(thetas))\n",
    "\n",
    "plt.figure(figsize=(12, 9))\n",
    "plt.plot(thetas, prior.pdf(thetas), label='Prior', c='blue')\n",
    "plt.plot(thetas, n*st.binom(n, thetas).pmf(h), label='Likelihood', c='green')\n",
    "plt.plot(thetas, post, label='Posterior', c='red')\n",
    "plt.xlim([0, 1])\n",
    "plt.xlabel(r'$\\theta$', fontsize=14)\n",
    "plt.ylabel('Density', fontsize=16)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
